INVESTIGATING DIFFICULT CONCEPTS IN SENIOR SECONDARY SCHOOL MATHEMATICS ...

International Journal of Academic Research and Reflection

Vol. 3, No. 6, 2015 ISSN 2309-0405

INVESTIGATING DIFFICULT CONCEPTS IN SENIOR SECONDARY SCHOOL MATHEMATICS CURRICULUM AS PERCEIVED BY STUDENTS

GLADYS CHARLES-OGAN (Ph.D) Department of Curriculum Studies and Educational Technology University of Port Harcourt Port Harcourt, NIGERIA

NCHELEM ROSEMARY GEORGE (Ph.D) Department of Mathematics/Statistics Ignatius Ajuru University of Education, Port Harcourt NIGERIA

ABSTRACT

This study employed the survey research design aimed at investigating difficult concepts in senior secondary school mathematics curriculum as perceived by students in Rivers state. The study was guided by two research questions and the sample for the study was 250 SS3 students. The instrument used for the collection of data was a 31-item questionnaire tagged Difficult Concept Identification Questionnaire in Mathematics (DCIQM). The instrument was validated and the reliability established using the test-retest method. The data obtained were analyzed using mean with the criterion mean set at 2.5.The findings of the study revealed that students identified some mathematics topics (longitude and latitude, bearing mensuration) as difficult topics. Based on the findings of the study, it was recommended amongst others that workshops should be organized to train mathematics teachers on the effective and efficient strategies that should be adopted for the teaching of the identified difficult mathematics concepts.

Keywords: Mathematics, Difficult topics, Curriculum, Students.

INTRODUCTION

Mathematics concepts are vast, interrelated and possess interconnected elements. The interrelationship of mathematical concepts can be identified in the use of elementary operations of division, ratios, percentage, addition, subtraction, translation of word problems and use of symbols across mathematics discourse while the interconnected elements according to Robertson and Wright (2014) are discovery and analysis of pattern, logical reasoning applied to systems and recognition and explanation of the underlying links between these systems. This suggestion exposes the requisite knowledge that underlies difficulty or non-difficulty of mathematics as a subject. Students of low logical reasoning and analytical prowess would, therefore, find certain concepts difficult. These students would have visual or dyslexic-type of difficulty which would inhibit their perception of pattern. In contrast, students of high reasoning ability and high intelligence may show competence in handling some concepts in mathematics but may also view some concepts as difficult.

The term "difficulty of concept" therefore, is not completely the inability of a student to obtain a pass mark in a collection of mathematics problems but what constitutes a `persistent hitch' and makes procedural approach to cognition of a mathematics concept a hideous task, all the time. In identifying students' difficulties with mathematics concepts, Robertson and Wright (2014) stated that students generally have intrinsic difficulty in mathematical reasoning, mathematical ideas and understanding basic mathematical concepts.

Elif (2003) also mentioned that students experience difficulties in constructing mathematical meanings of symbols. This view was re-emphasized by Hiebert and Carpenter (1992) and Janvier, Giorardon and Morand (1993). The researchers emphatically stated that most of the

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International Journal of Academic Research and Reflection

Vol. 3, No. 6, 2015 ISSN 2309-0405

difficulty in understanding symbols comes from the fact that the symbols might take on different meanings in different settings.

The conceptual knowledge in mathematics requires adherence to an algorithm that leads the solver through a correct process to a correct answer. During instruction, students should be allowed to actively participate in each step of a problem solving algorithm for formalization and effective practice. Some students' difficulties can be attributed to inappropriate representation and handling of problems, such as fractions, ratio, extrapolation and erroneous algorithm (Silver, 1986; Ben ? Zeev, 1996).

Some problems such as mathematics anxiety among students and attitude towards mathematics learning have been identified by researchers to be inherent in students. Mensah, Okyere and Kuranchie (2013) explains that attitude as a concept is concerned with an individual's way of thinking, acting and behaving and has serious implication on the learner. However, Yara (2009) posits that teachers with positive attitude, towards mathematics can stimulate favourable attitudes in their students. The student attitude towards a learning process whether innate or emulated, reshapes his behavior in the classroom and an emotional disposition towards mathematics. Hart (1989) consider attitude toward mathematics from multidimensional perspectives and defined an individuals' attitude toward mathematics as a more complex phenomenon characterized by the emotions that he associates with mathematics; his beliefs about mathematics and how he behaves towards mathematics. This study is therefore aimed at identifying these difficult topics in senior secondary school mathematics curriculum as perceived by students in Rivers State of Nigeria.

Statement of the Problem

Mathematics plays a key role in shaping how individuals deal with the various spheres of life, be it private, social or cooperate. A cursory look at the national curriculum for mathematics reveals the concepts applicability of the mathematics knowledge in our formal and informal daily activities. Students' of the subject matter have challenges to effectively learn mathematical processes.

The WAEC chief examiners' report has shown that there is over a decade-long poor performance of students in mathematics despite improved teaching methods and motivational learning strategies. This trend is frustrating to students' aspiration for higher education in areas where a credit in mathematics is required and general cognition of the subject. It is therefore, necessary to allow the student indicate what constituted their difficulty in the subject area and the possible cause of such difficulties.

Purpose of the Study

The purpose of the study was to investigate the difficult concepts in senior secondary school mathematics curriculum as perceived by students. Specifically, the objectives of the study are to:

1. Find out the difficult concepts in mathematics in the senior secondary school curriculum as perceived by the students.

2. Ascertain the causes of the identified difficult mathematics concepts in the senior secondary school curriculum as perceived by the students.

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International Journal of Academic Research and Reflection Research Questions

Vol. 3, No. 6, 2015 ISSN 2309-0405

The following research questions guided the study: 1. What mathematics concepts do students perceive as difficult in the senior secondary school mathematics curriculum? 2. What are the possible causes of the identified difficult mathematics concepts in the senior secondary school curriculum as perceived by the students?

Methodology

Descriptive survey design was adopted for the study using the Difficult Concept Identification Questionnaire in Mathematics (DCIQM). The sample consisted of two hundred and fifty (250) SS3 students from eight public coeducational senior secondary schools in Rivers State. The instrument was based on the current national mathematics curriculum for senior secondary school. DCIQM was researcher constructed and made up of two sections, A and B. Section A measured the difficult mathematics concepts as perceived by students while section B measured the possible causes of the identified concept difficulty. Section A was made up of twenty one items on a 4-point scale of Very Difficult =4, Difficult =3, Less Difficult =2 and Not Difficult =1. Section B was made up of ten items on a 4-point Likert scale of Strongly Agree =4, Agree =3, Disagree = 2 and Strongly Disagree =1.The face and content validity of the instrument was ascertained through a peer review of mathematics educators. The instrument was established reliable with a reliability index of 0.75 using the test-retest method. The data obtained were analyzed using mean. The criterion mean for each item in both sections of DCIQM was 2.5.

RESULTS AND DISCUSSION Research Question I: What mathematics concepts do students perceive as difficult in the senior secondary school mathematics curriculum?

Table 1: Students' Perception of Difficult concepts in Mathematics

Rating: VD ? 4, D ? 3, LD ? 2, ND ? 1

S/N

Topic

Very Difficult Less Non-

difficult

difficult difficult

Decision

N

N

1. Number Base System

- Conversion of decimal fraction from other bases to base 10 -

-

N 240

N 130

Not 1.48 diff

- Apply Number Base in Computer

Programming

2. Modular arithmetic - Simple or basic operations - Solving Problems in Standard Form

- Laws of indices and Problems involving indices e.g. ax x ay = ax+y etc.

3. Logarithms - Indices and logarithms

- Graphs of y = 10x

256 153

248 31

-

-

-

-

12

36

362

53

4

-

428

32

-

-

-

-

164 156 314

-

2.59 Diff

1.85 Not

diff 1.86 Not

diff

2.54 Diff

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International Journal of Academic Research and Reflection

Vol. 3, No. 6, 2015 ISSN 2309-0405

- Use of logarithm tables in calculation i division powers and roots e.g. 214.3 x 3308

83

416

21

2.08 NotD iff

- solve problems related to capital market (Application of 52

42

logarithms)

226

1.0

4. Set theory - Identify types of set

201 93

200

63

- Use of venn diagram

208 102

200

64

- Use venn diagram to solve real life problems - E.g.

208 93

200

63

1.66 Not Diff

2.26. Not diff

2.29 Not diff

2.26 Not diff

Find x?

2X 4 10

5. Simple Equations and variations. - Problems involving in verse variation

- Joint variation and

- Application of variation

- Simple equations and variations

- Simultaneous Equation

- Quadratic equation:

- Factorization of Quadratic Equation

- One linear one quadratic simultaneous equation.

- Forming Quadratic equations with known roots

- Solve word problems in Quadratic Equation.

6. Construction - Bisection of lines and apples

- Constructing angles

- Construction of equidistance point

- Locus of moving points

- Proofs of some Basic theorems

7. Trigonometrical ratio - Solve problems involving use of sine and cosine formula. - Ratios of 30, 40 and 60

- Solving problems using Trigonometrical Ratios

- Drawing graphs of sine and cosine of angles.

132 27

326

55

16

33

16

33

-

-

-

-

-

-

-

-

64

96

112

3

116

54

-

-

360

56

360

56

128

158

362

8.69

400

50

242

149

206

74

222

100

206 100

252

124

-

-

264

118

-

-

46

217

80

168 218

154

480 342 160

41

-

-

367

139

-

-

384

133

-

-

416

117

480 342 160

41

2.16 Not diff

1.86 Not diff

1.86 NotD iff

1.36 NotD iff

1.72 NotD iff

1.80 NotD iff

1.56 NotD iff

1.96 NotD iff

1.87 NotD iff

1.90 NotD iff

1.49 NotD iff

1.53 NotD iff

1.05 NotD iff

2.48 NotD iff

4.05 Diff

2.02 NotD iff

2.06 NotD iff

2.13 NotD iff

4.05 Diff

8. Mensuration. - Find length of arc practically

428 372 78

40

2.47 Not

Diff

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International Journal of Academic Research and Reflection

- Determine perimeter of a circle, segments of circles

76

171

- Length of arcs using formula - Area of a sector

-

306

-

-

- Find area of triangle and subtract area of circle e.g.

-

-

- Relationship between surface area of a cone and sector of a 172 168 circle.

9. Statistics

-

-

- Construction of frequency distribution curve, histograms, bar

chart and line graphs; pie chart

- Frequency polygon (O give)

-

-

10. Approximations - Calculate percentage errors

- Degree of accuracy

-

-

-

-

11. Sequence and series - Arithmetic progression

- Geometric progression

204 132

92

58

- Practical problems on AP and G.P

212 114

12. Graphical solutions of - Quadratic and simultaneous equations

-

300

- Gradient of a curve - Drawing tangents to a curve, at a given point.

576 -

13. Inequalities, graphs and problems in inequalities. - Linear inequalities in two variables

142 165

- Deducing maximum and minimum values of inequality graphs -

-

- Introduction to linear programming

232 198

14. Measuration II: Chord and theorems: Angles subtended at the

centre, Angles subtended by chords in a circles, Angles in 432 336

alternate segments.

15. Circle theorems ? Angles at centre is twice that at the

circumstance

504 246

- Problems involving circle theorems

16. Derivation of sine and cosine rule.

616 108

- Bearings ? angle of elevation and depression.

- Practical problems on bearings.

720 363

17. Measures of central tendency ? mean, median, mode or

ungrouped data.

416 363

- Def. of range, variance, standard deviation practical application

in capital market reports.

- Areas of applications

480 423

18. The concept of probability

-

-

- Practical example; list chance instruments (dice, coin, park of

playing cards)

19. Matrices and Determinants

-

189

- Transpose of determinants

- Solving simultaneous equations using determinants

584 249

Vol. 3, No. 6, 2015 ISSN 2309-0405

280

109

2.54 Diff

226

100

2.53 Diff

422

114

2.14 Not

Diff

570

80

2.60 Diff

344

97

3.12 Diff

580

35

2.46 Not Diff

568

41

2.46 Not

Diff

216

109

1.31 Not

Diff

300

100 1.60 Not

Diff

336

61

2.93 Diff

246

71

2.27 Not

Diff

122

-

1.75 Not

Diff

140

170

2.32 Not

diff

208

29

3.25 Diff

344

55

2.82 Diff

560

45

2.42 Not Diff

202

100

2.93 Diff

3.45 Diff

-

105

214

-

3.86 Diff

200

60

3.94 Diff

28

10

160

20

4.46 Diff

Diff 3.84

128

-

4.12 Diff

328

161

1.96 Not

Diff

284

120

2.37 Not

Diff

192

-

4.10 Diff

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